In Paris, most people who are now biking are people who would have taken public transportation before, so the amount of cars on the roads is roughly the same as before.
I don't live there anymore but I grew up in Paris -
I knew absolutely nobody living in Paris driving to another location in Paris. It's always been metro first, bicycle sometime. Almost all of the passenger car you see in Paris are people driving from the suburb.
Many cars in Paris are driven by people commuting to Paris from outside. There is a real fracture between suburbans (who don't vote for those changes happening in Paris) and city residents who votwd for them.